移动问题及其推广

<正>在学习排列组合一章时,我们常会遇到移动问题,有这样一个例子.【例1】一只蚂蚁在平面直角坐标系内,从原点出发沿x轴移动,每次可向正方向或负方向移动一个单位,经过5次移动,蚂蚁移动到(3,0)点处,蚂蚁不同的移动方法共有几种?     

基于位置数据的用户多周期移动行为挖掘

挖掘位置数据中的用户行为规律是大数据时代的研究热点之一.现有研究主要关注于用户在某时刻出现在某地点的行为,对于用户从一个地点移动到另一个地点的动态行为研究较为空缺.提出一种挖掘位置数据中用户移动行为的算法可以发现用户的多个周期移动行为,描述用户在时空上的移动规律.首先,利用离散傅里叶变换和自相关系数检测用户移动行为的周期,在这一过程中,利用Apriori性质减少计算复杂度;而后提出用户移动行为的生成模型,估计用户的移动行为概率矩阵,考虑到观测数据的稀疏性,采用带全局限制的动态时间规整距离对不同时间段的行为进行聚类以发现用户的多个周期移动行为.最后,我们选取某市公共自行车系统收集的位置数据进行实证分析,结果表明,新方法能有效地挖掘用户的多个周期移动行为,进一步地,通过归纳可以得到用户群体在周期移动行为上的主要特征.     

用“运动变化”和“数量关系”观察、判定位置关系

<正>我们先回顾一下研究直线和圆的位置关系的过程和方法.1.直线和圆有几种位置关系?和哪些数量有关呢?(1)圆心的位置和圆的大小不变,移动直线,请你观察直线和圆有几种位置关系?什么数量在变化?随着直线的移动,直线和圆出现三种不同的位置关系,如图1所示.作OD⊥l于D,设OD=d,可以发现,在直线移动的过程中,圆心     

满足条件的移动时间问题

在数学中考题中,我们常常会碰到下列移动问题:即一个(或两个)点在线段上移动,当移动时间是多少时,使这两个动点之间的距离等于已知量,或使某两条线段相等,或使某两个三角形相似等等这样的问题.解决这类问题的基本方法     

基于分层序列的移动电子商务推荐系统策略研究

移动互联网环境下,移动电子商务快速发展,移动推荐系统成为解决移动信息过载的主要技术和手段.移动电子商务推荐系统中用户策略选择是一个典型的多目标决策问题,目标之间也存在一定的矛盾.基于移动推荐系统的这种特征,借助分层序列法算法的思想,通过元数据的标准化处理,结合移动电子商务中的位置上下文信息获取推荐数据,得到满足用户多目标需求的推荐结果.方法的提出为移动电子商务推荐系统的研究提出了一种新的推荐策略.     

轮式移动舞台机器人双模模型预测控制北大核心CSCD

针对轮式移动舞台机器人的快速镇定和移动区域约束控制问题,提出一种快速双模模型预测控制(MPC)算法.考虑轮式移动舞台机器人的位姿约束和速度约束,采用控制Lyapunov函数概念和极坐标系模型设计模型预测控制算法.利用移动舞台机器人与目标的距离、瞄准角和方位角构造一个控制Lyapunov函数,建立移动舞台机器人的一个解析双模结构MPC控制器,再引入自由变量,参数化预测控制变量,降低双模MPC在线优化计算量.在约束条件下,建立了轮式移动舞台机器人闭环系统稳定性和MPC递推可行性理论结果.最后,通过与常规MPC比较,仿真验证所提算法的有效性和优越性.     

Moving mesh method for a reaction-diffusion equation with traveling heat source on unbounded domain

对无界区域上带移动热源的反应扩散方程提出了局部吸收边界条件.移动网格方法对导出的有界区域问题进行了求解.数值例子显示了当热源移动的速度比较慢的时候,方程会在有限时间内发生爆破现象.而当热源移动的速度足够快时,爆破现象不会发生.数值例子验证了新方法的有效性和精确性.     

基于移动增值业务的电信服务链建模研究

以高速发展的移动互联网为背景,研究了由一个服务提供商和一个电信运营商组成的移动增值业务电信服务链商业模式.考虑了电信运营商促销对于移动增值业务市场需求的影响,构建了电信运营商主导的移动增值业务博弈模型,给出了不同合作模式情形下服务提供商和电信运营商的最优决策.     

基于特定群体的移动商务消费者信任影响因素分析

消费者信任是影响移动商务发展的关键因素,针对国内移动商务发展的现状,构建了以高校大学生为研究对象的移动商务消费者信任影响因素模型,模型包括消费者个人、产品、移动商家、移动技术、网站媒介以及制度保障6个方面的内容,并据此设计了网络调查问卷,累计收集了219份有效数据.实证分析表明:对高校大学生而言,移动终端设备的易用性是影响消费者信任最关键的因素,其次是消费者对移动互联网和移动商家的熟悉程度,第三是移动商务产品的价格差异;最后根据数据分析结果提出了改善移动商务消费者信任的建议.     

移动平均亚式期权定价研究

移动平均期权是价格依赖于标的资产移动平均价格的奇异期权,其定价依赖于每个窗口内的标的资产的价格,随着窗口不断向前滚动,就会有无穷多个移动平均过程,而无穷多个移动平均过程是无限维的非马尔科夫问题,因此该研究具有较大的挑战性,研究成果较少.移动平均亚式期权多用于场外的能源(石油,天然气,电力)衍生品合约,因此研究其定价和数值计算方法具有一定的理论意义和实践价值.本文以移动平均亚式期权为研究对象,运用截断的拉盖尔序列的方法,通过估计近似测度,以有限维的移动平均过程近似无限维的移动平均过程.随着拉盖尔序列所取阶数的增加,有限维移动平均对无限维移动平均的近似效果将越来越好.在得到近似的有限维标的资产价格的移动平均过程后,移动平均期权的定价转化为一个美式期权最优停时问题,本文用最小二乘蒙卡解决美式移动平均期权的最优行权问题,从而给移动平均亚式期权定价,数值分析表明通过对比拉盖尔方法和蒙卡模拟的方法,拉盖尔方法的稳定性较高.而对于固定执行价格和浮动执行价格移动平均亚式期权,都存在随着窗口长度增加,期权价格上涨的递增关系,这与一般的逻辑推断吻合.数值计算结果还表明当窗口长度增加到期权整个有效期时,移动平均亚式期权就退化为相应的亚式期权.进一步证明了该方法的正确性.     

A regularized point cloud registration approach for orthogonal transformations

An important part of the well-known iterative closest point algorithm (ICP) is the variational problem. Several variants of the variational problem are known, such as point-to-point, point-to-plane, generalized ICP, and normal ICP (NICP). This paper proposes a closed-form exact solution for orthogonal registration of point clouds based on the generalized point-to-point ICP algorithm. We use points and normal vectors to align 3D point clouds, while the common point-to-point approach uses only the coordinates of points. The paper also presents a closed-form approximate solution to the variational problem of the NICP. In addition, the paper introduces a regularization approach and proposes reliable algorithms for solving variational problems using closed-form solutions. The performance of the algorithms is compared with that of common algorithms for solving variational problems of the ICP algorithm. The proposed paper is significantly extended version of Makovetskii et al. (CCIS 1090, 217–231, 2019).

     

Some Results on Greedy Embeddings in Metric Spaces

Geographic Routing is a family of routing algorithms that uses geographic point locations as addresses for the purposes of routing. Such routing algorithms have proven to be both simple to implement and heuristically effective when applied to wireless sensor networks. Greedy Routing is a natural abstraction of this model in which nodes are assigned virtual coordinates in a metric space, and these coordinates are used to perform point-to-point routing.     

Motion Control Algorithms for Simple Mechanical Systems with Symmetry

We treat underactuated mechanical control systems with symmetry, taking the viewpoint of the affine connection formalism. We first review the appropriate notions and tests of controllability associated with these systems, including that of fiber controllability. Secondly, we present a series expansion describing the evolution of the trajectories of general mechanical control systems starting from nonzero velocity. This series is then used to investigate the behavior of the system under small-amplitude periodic forcing. On this basis, motion control algorithms are designed for systems with symmetry to solve the tasks of point-to-point reconfiguration, static interpolation and stabilization problems. Several examples are given and the performance of the algorithms is illustrated in the blimp system.     

On a geometrically exact theory for contact interactions

The focus of the contribution is on the development of the unified geometrical formulation of contact algorithms in a covariant form for various geometrical situations of contacting bodies leading to contact pairs: surface-to-surface, line-to-surface, point-to-surface, line-to-line, point-to-line, point-to-point. The computational contact algorithm will be considered in accordance with the geometry of contact bodies in a covariant form. This combination forms a geometrically exact theory of contact interaction, see [1]. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Dynamic TCP acknowledgment in the LogP model

When messages, which are to be sent point-to-point in a network, become available at irregular intervals, a decision must be made each time a new message becomes available as to whether it should be sent immediately or if it is better to wait for more messages and send them all together. Because of physical properties of the networks, a certain minimum amount of time must elapse in between the transmission of two packets. Thus, whereas waiting delays the transmission of the current data, sending immediately may delay the transmission of the next data to become available even more. We propose a new quality measure and derive optimal deterministic and randomized algorithms for this on-line problem.     

Optimality with telecommunications network

This paper studies a telecommunications company's optimal networkinvestment strategies. The objective of the company is to maximizethe value of the network. According to our numerical exampleswe are not able to consider a single point-to-point connectionseparately from the network, because the network demands andcapacities affect each other. Therefore, the whole network structurehas to be considered in the point-to-point investments.     

Unified approach to unconstrained minimization via basic matrix factorizations

Important classes of algorithms for unconstrained minimization, when applied to a quadratic with Hessian A, may be regarded as alternative ways to effect certain basic matrix factorizations of or with respect to A. This approach enables a unified presentation of many existing algorithms and suggests some new algorithms. Two basic underlying factorizations are of particular interest—tridiagonalization coupled with Cholesky factorization and the Gram-Schmidt or QR factorization.     

Parameterized complexity of spare capacity allocation and the multicost Steiner subgraph problem

We study the computational complexity of the Spare Capacity Allocation problem arising in optical networks that use a shared mesh restoration scheme. In this problem we are given a network with edge capacities and point-to-point demands, and the goal is to allocate two edge-disjoint paths for each demand (a working path and a so-called restoration path, which is activated only if the working path fails) so that the capacity constraints are satisfied and the total cost of the used and reserved bandwidth is minimized. We focus on the setting where we deal with a group of demands together, and select their restoration paths simultaneously in order to minimize the total cost. We investigate how the computational complexity of this problem is affected by certain parameters, such as the number of restoration paths to be selected, or the treewidth of the network graph. To analyze the complexity of the problem, we introduce a generalization of the Steiner Forest problem that we call Multicost Steiner Subgraph. We study its parameterized complexity, and identify computationally easy and hard cases by providing hardness proofs as well as efficient (fixed-parameter tractable) algorithms.     

AHP的算法及其比较分析

本文简述了运用AHP方法解决实际问题时的基本步骤、排序原理。重点介绍了AHP的六种常用算法的基本原理、算法步骤,并对这几种算法作了初步的比较与分析。     

The intermediate disorder regime for Brownian directed polymers in Poisson environment

We consider the Brownian directed polymer in Poissonian environment in dimension 1+1, under the so-called intermediate disorder regime (Alberts et al., 2014), which is a crossover regime between the strong and weak disorder regions. We show that, under a diffusive scaling involving different parameters of the system, the renormalized point-to-point partition function of the polymer converges in law to the solution of the stochastic heat equation with Gaussian multiplicative noise. The Poissonian environment provides a natural setting and strong tools, such as the Wiener–Itô chaos expansion (Last and Penrose, 2017), which, applied to the partition function, is the basic ingredient of the proof.